Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The triangles in the figure above are equilateral and the [#permalink]

Show Tags

05 Apr 2008, 22:14

3

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

63% (02:23) correct
37% (01:14) wrong based on 503 sessions

HideShow timer Statistics

Attachment:

2triangles.GIF [ 1.58 KiB | Viewed 8915 times ]

The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K? (A) 3/4K (B) 2/3K (C) 1/2K (D) 1/3K (E) 1/4K

A would be my answer. Area of shaded = Area of Large - Area of Small Give: Area of Large = K We need to find Area of Small in term of K. Triangle area = 1/2 * base * height and since a side of the large triangle is twice larger than a side of small triangle, we are dealing with (1/2) * (1/2) = 1/4 factor. Therefore, Area of shaded = K - K/4 = 3K/4

16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K? (A) 3/4K (B) 2/3K (C) 1/2K (D) 1/3K (E) 1/4K

A.

the ratio tells you that the larger also is a equilateral triangle. Length of small one is a length of larger one is b a =b/2

the larger arear = K= b^2*(square root(3)/4) I called square root(3)/4 S the smaller area = a^2 *S = S*b^2 /4 = K/4

Another way to do this! Theorem : If there are Two similar triangles with sides in Ratio : S1 : S2 - then their areas are in the ratio S1^2 : S2 ^2 => Area of Larger : Area of Smaller = S1^2 : S2^2 => K : As = 2^2 : 1 => As = k/4

Therefore, Area of the shaded region : K-K/4 = 3k/4

16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K? (A) 3/4K (B) 2/3K (C) 1/2K (D) 1/3K (E) 1/4K

Yes, the property given above is very useful. It states: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{S^2}{s^2}\).

As both big and inscribed triangles are equilateral then they are similar, so \(\frac{AREA}{area}=\frac{S^2}{s^2}=\frac{2^2}{1^2}=4\), so if \(AREA=K\) then \(area=\frac{K}{4}\) --> the area of the shaded region equals to \(area_{shaded}=K-\frac{K}{4}=\frac{3K}{4}\).

We have that \(\frac{AREA}{area}=4\). Now, since \(AREA=K\) then \(\frac{K}{area}=4\) --> \(area=\frac{K}{4}\) --> the area of the shaded region equals to \(area_{shaded}=K-\frac{K}{4}=\frac{3K}{4}\).

Re: The triangles in the figure above are equilateral and the [#permalink]

Show Tags

09 Jun 2013, 22:14

1

This post received KUDOS

jimmylow wrote:

Attachment:

2triangles.GIF

The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4K (B) 2/3K (C) 1/2K (D) 1/3K (E) 1/4K

The easiest way to solve this one would be by picking numbers. Lets say each side of the larger triangle is 6 and given the ratio 2:1 each side of smaller triangle then is 3. Area of an equilateral triangle can be calculated using formula: \(s^2(\sqrt{3})/4\) where s = side. So area of large triangle = k = \(9(\sqrt{3})\) and area of small triangle = \(9(\sqrt{3})/4\) = \(k/4\). So the area of the smaller triangle is 1/4 the area of the large triangle. Area of shaded region=\(k-k/4\) = \(3/4k\)
_________________

___________________________________________ Consider +1 Kudos if my post helped

Re: The triangles in the figure above are equilateral and the [#permalink]

Show Tags

01 Oct 2015, 23:41

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Let side of larger eq. triangle=2X area=sq.root3/4*(2X)^2------->sq.root3*x^2------(A) therefore side of smaller eq. triangle=X(given ratio=2/1) area of smaller- sq.root3*x^2/4 area of shaded part=larger-smaller triangle =sq.root3*x^2-sq.root3*x^2/4------------>sq.root3*x^2(1-1/4) substituting from eq. (A) area of shaded part=3/4K Ans A

gmatclubot

Re: The triangles in the figure above are equilateral and the
[#permalink]
20 Jul 2016, 11:37

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Term 1 has begun. If you're confused, wondering what my post on the last 2 official weeks was, that was pre-term. What that means is that the school...